Discrete RV and Binomial Prob. Dist. + Sigma Notation

Front

What is the mean of a binomial distribution?

Back

The mean (μ) of a binomial distribution is calculated using the formula μ = n * p, where n is the number of trials and p is the probability of success.

Front

Calculate the mean for n=50 and p=0.4.

Back

Mean = 50 * 0.4 = 20.

Front

What is the standard deviation of a binomial distribution?

Back

The standard deviation (σ) of a binomial distribution is calculated using the formula σ = √(n * p * q), where q = 1 - p.

Front

Calculate the standard deviation for n=50, p=0.4.

Back

Standard deviation = √(50 * 0.4 * 0.6) ≈ 5.787.

Front

What is a probability distribution?

Back

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

Front

Identify a characteristic of a valid probability distribution.

Back

The sum of all probabilities in a probability distribution must equal 1.

Front

What is the complement of an event in probability?

Back

The complement of an event A, denoted as A', is the event that A does not occur. If p = P(A), then q = P(A') = 1 - p.

Front

If p = 82%, what is q?

Back

q = 1 - p = 1 - 0.82 = 0.18.

Front

What is Sigma notation?

Back

Sigma notation (Σ) is a way to represent the sum of a series of terms, where the index of summation indicates the starting and ending values.

Front

How do you calculate the sum using Sigma notation?

Back

To calculate the sum using Sigma notation, identify the function to be summed and the limits of summation, then evaluate the function for each integer value in the range.